US 20030208327 A1 Abstract Methods are provided for embedding and/or de-embedding a network having an even number of ports into a device under test (DUT) having an odd number of ports. For example, a four-port network can be embedded/de-embedded into/from a three-port device under test (DUT). This is accomplished by embedding a virtual circulator into the three-port DUT to thereby generate an artificial four-port device. The four-port network is then embedded/de-embedded into/from the artificial four-port device to thereby generate a composite four-port device. The virtual circulator is then de-embedded from the composite four-port device to thereby generate a composite three-port device that is equivalent to the four-port network embedded/de-embedded into/from the three-port DUT.
Claims(20) 1. A method for embedding a four-port network into a three-port device under test (DUT), the method comprising the steps of:
(a) embedding a circulator into the three-port DUT to thereby generate an artificial four-port device; (b) embedding the four-port network into the artificial four-port device to thereby generate a composite four-port device; and (c) de-embedding the virtual circulator from the composite four-port device to thereby generate a composite three-port device that is equivalent to the four-port network embedded into the three-port DUT. 2. The method of 3. The method of (a.1) acquiring a 3×3 scattering-matrix for the three-port DUT; and (a.2) generating a 4×4 scattering-matrix based on characteristics of the virtual circulator and based on the 3×3 scattering-matrix for the three-port DUT, the 4×4 scattering-matrix being representative of the artificial four-port device. 4. The method of (b.1) generating a 4×4 transfer-matrix for the artificial four-port device based on the 4×4 scattering matrix representative of the artificial four-port device; (b.2) acquiring a 4×4 scattering-matrix for the four-port network; (b.3) generating a 4×4 transfer-matrix for the four-port network based on the 4×4 scattering matrix for the four-port network; (b.4) multiplying the 4×4 transfer-matrix for the four-port network with the 4×4 transfer-matrix for the artificial four-port device to thereby produce a composite 4×4 transfer-matrix; and (b.5) generating a composite 4×4 scattering-matrix based on the composite 4×4 transfer-matrix, the 4×4 composite scattering-matrix being representative of the four-port artificial device with the four-port network embedded into it. 5. The method of 6. The method of 7. The method of 8. The method of 9. A method for embedding a network into a device under test (DUT) having an odd number of ports, the method comprising the steps of:
(a) embedding a circulator into the DUT to thereby generate an artificial device having an even number of ports; (b) embedding the network into the artificial device to thereby generate a composite device; and (c) de-embedding the virtual circulator from the composite device to thereby generate a further composite device that is equivalent to the network embedded into the DUT. 10. The method of 11. A method for de-embedding a four-port network from a three-port device under test (DUT), the method comprising the steps of:
(a) embedding a circulator into the three-port DUT to thereby generate an artificial four-port device; (b) de-embedding the four-port network from the artificial four-port device to thereby generate a composite four-port device; and (c) de-embedding the virtual circulator from the composite four-port device to thereby generate a composite three-port device that is equivalent to the four-port network de-embedded from the three-port DUT. 12. The method of 13. The method of (a.1) acquiring a 3×3 scattering-matrix for the three-port DUT; and (a.2) generating a 4×4 scattering-matrix based on characteristics of the virtual circulator and based on the 3×3 scattering-matrix for the three-port DUT, the 4×4 scattering-matrix being representative of the artificial four-port device. 14. The method of (b.1) generating a 4×4 transfer-matrix for the artificial four-port device based on the 4×4 scattering matrix representative of the artificial four-port device; (b.2) acquiring a 4×4 scattering-matrix for the four-port network; (b.3) generating a 4×4 transfer-matrix for the four-port network based on the 4×4 scattering matrix for the four-port network; (b.4) multiplying the 4×4 transfer-matrix for the four-port network with an inverse of the 4×4 transfer-matrix for the artificial four-port device to thereby produce a composite 4×4 transfer-matrix; and (b.5) generating a composite 4×4 scattering-matrix based on the composite 4×4 transfer-matrix, the 4×4 composite scattering-matrix being representative of the four-port network de-embedded from the four-port artificial device. 15. The method of 16. The method of 17. The method of 18. The method of 19. A method for de-embedding a network from a device under test (DUT) having an odd number of ports, the method comprising the steps of:
(a) embedding a circulator into the DUT to thereby generate an artificial device having an even number of ports; (b) de-embedding the network from the artificial device to thereby generate a composite device; and (c) de-embedding the virtual circulator from the composite device to thereby generate a further composite device that is equivalent to the network de-embedded from the DUT. 20. The method of Description [0001] 1. Field of the Invention [0002] The present invention relates to methods for embedding and/or de-embedding networks when, for example, making measurements using a vector network analyzer (VNA). More particularly, the present invention relates to calculations for embedding and/or de-embedding networks that are not directly amenable to chain matrix calculations, such as three-port devices and semi-balanced devices with an odd number of ports. [0003] 2. Description of the Related Art [0004] Measurements of a device under test (DUT) using a VNA may not always be performed in a desired test environment. This is because it maybe too time intensive and/or costly to measure a DUT in a desired test environment. Accordingly, a DUT is often measured in a different environment for reasons of expediency and/or practicality, thereby requiring the use of embedding or de-embedding techniques to correct the effects of the test environment. For example, a DUT may be in a test fixture or connected via wafer probes when measurements of the DUT are made, thereby requiring the removal of the effects of the fixture or probes from the measured data for a truer picture of actual DUT performance. De-embedding techniques allows this task (i.e., removal of effects) to be performed computationally. This concept is shown in FIG. 1A. In another example, a customer may desire to see what the performance of a DUT would be with a specific matching network attached. However it may be impractical to attach the matching network during manufacturing for cost reasons. Embedding techniques allow this task (i.e., attaching the matching network) to be performed computationally. This concept is shown in FIG. 1B. [0005] While most commercial simulators use nodal wave analysis or similar techniques for computing composite network results, these approaches may not be needed or wanted (e.g., based on computational or memory needs) for certain specific applications. Among these applications are embedding or de-embedding networks to/from a measurement. For two port devices, a chain matrix or cascading computation using transfer-matrices has been used to perform embedding and de-embedding. The concept is to re-arrange standard scattering-parameters (S-parameters) to form a pair of new matrices (termed T for transfer matrices) that can be multiplied for embedding and form the equivalent to the networks being concatenated or cascaded (i.e., one network being embedded). Multiplying by the inverse of the T-matrix (i.e., T [0006] Transfer-matrices (also known to as transmission matrices) are made up of T-parameters (also known as chain-scattering-parameters and scattering-transfer-parameters) that are defined in a manner analogous to S-parameters except the dependencies have been switched to enable the cascading discussed above. In both cases the wave variables are defined as a [0007] where, [0008] a [0009] a [0010] b [0011] b [0012] S [0013] S [0014] S [0015] S [0016] (Note that the set of S-parameters S [0017] The T-formulation is a bit different to allow for cascading. More specifically, in the T-formulation, b [0018] Two cascaded two-port networks [0019] The equations for computing the T-parameters in terms of the S-parameters (and vice versa) can be mathematically derived. The results are shown below in Equations 3 and 4.
[0020] The above analysis and equations are useful for embedding and/or de-embedding two-port networks. A concept for embedding and/or de-embedding four-port networks is disclosed in commonly invented and assigned U.S. patent application Ser. No. 10/050,283, entitled “Methods for Embedding and De-Embedding Balanced Networks,” filed Jan. 15, 2002, which in incorporated herein by reference in its entirety. FIG. 4 illustrates such a four-port network [0021] The four-port network of FIG. 4 may be a balanced circuit. A balanced circuit, as defined herein, is a circuit that includes a pair of ports that are driven as a pair, with neither port of the pair being connected to ground. Examples of balanced circuits are circuits that have differential or common mode inputs. A balanced circuit need not be completely symmetrical. Balanced circuits have often been used in the pursuit of lower power consumption, smaller size, better electromagnetic interference (EMI) behavior and lower cost. This is especially true for consumer electronics. The behavior of the class of balanced devices are illustrated in FIGS. [0022] The next obstacle/question is how to handle cascaded symmetric networks, such as one including a three-port network with one single-ended port and a balanced port pair as shown in FIG. 6. The desire here is to embed or de-embed a four-port network [0023] Embodiments of the present invention are directed to methods for embedding a network having an even number of ports into a device under test (DUT) having an odd number of ports. A circulator is embedded into the DUT to thereby generate an artificial device having an even number of ports. The network is then embedded into the artificial device to thereby generate a composite device. Finally, the circulator is de-embedded from the composite device to thereby generate a further composite device that is equivalent to the network embedded into the DUT. The above mentioned circulator need not be an actual circulator, but rather, can be a virtual circulator. [0024] Embodiments of the present invention are also directed to methods for de-embedding a network having an even number of ports from a DUT having an odd number of ports. A circulator (e.g., a virtual circulator) is embedded into the DUT to thereby generate an artificial device having an even number of ports. The network is then de-embedded from the artificial device to thereby generate a composite device. Finally, the circulator is de-embedded from the composite device to thereby generate a further composite device that is equivalent to the network de-embedded from the DUT. [0025] A specific embodiment of the present invention is directed to a method for embedding a four-port network into a three-port DUT. For example, this embodiment can be used to embed the four-port network into a balanced side of the three-port DUT. A circulator (e.g., a virtual circulator) is embedded into the three-port DUT to thereby generate an artificial four-port device. The artificial four-port device enables the use of four-port embedding techniques. The four-port network is then embedded into the artificial four-port device to thereby generate a composite four-port device. The circulator is then de-embedded from the composite four-port device. The result is a composite three-port device that is equivalent to the four-port network embedded into the three-port DUT. [0026] Another embodiment of the present invention is directed to a method for de-embedding a four-port network from a three-port DUT. For example, this embodiment can be used to de-embed the four-port network from a balanced side of the three-port DUT. A circulator (e.g., virtual circulator) is embedded into the three-port DUT to thereby generate an artificial four-port device. The artificial four-port device enables the use of four-port de-embedding techniques. The four-port network is then de-embedded from the artificial four-port device to thereby generate a composite four-port device. The circulator is then de-embedded from the composite four-port device. The result is a composite three-port device that is equivalent to the four-port network de-embedded from the three-port DUT. [0027] The features, objects, and advantages of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify the same or similar elements throughout and wherein: [0028]FIG. 1A is a diagram illustrating the concept of de-embedding; [0029]FIG. 1B is a diagram illustrating the concept of embedding; [0030]FIG. 2 is a diagram illustrating the incident and reflective waves of a two-port network; [0031]FIG. 3 is a diagram illustrating two cascaded two-port networks; [0032]FIG. 4 is a diagram illustrating a four-port network; [0033] FIGS. [0034]FIG. 6 is a diagram illustrating the cascading of a three-port device under test (DUT) and a four-port network; [0035]FIG. 7 is a diagram illustrating a splitter added to the three-port DUT of FIG. 6; [0036]FIG. 8 is a diagram illustrating a circulator added to the three-port DUT of FIG. 6, to thereby produce an artificial four-port DUT; [0037]FIG. 9 is a diagram illustrating the embedding of a four-port network into an artificial four-port DUT, to thereby produce a composite four-port network; [0038]FIG. 10 is a flow diagram describing a method for embedding a four-port network into a 3-port DUT, according to an embodiment of the present invention; [0039]FIG. 11 is a flow diagram describing a method for de-embedding a four-port network from a 3-port DUT, according to an embodiment of the present invention; and [0040]FIG. 12 is a flow diagram that is used to describe additional details of steps shown in FIGS. 10 and 11. [0041] In the description that follows, the terms network, circuit, device and structure are used interchangeably. [0042] Among other things, the present invention addresses the obstacle/question of how to handle incompletely balanced networks, such a three-port network with one balanced port as shown in FIG. 6. Specifically, as mentioned above, a desire is to embed or de-embed four-port network [0043] One possibility for embedding/de-embedding four-port network denom= [0044] Thus, if all of the S-parameters associated with a single port were zeroed out (to make the four-port network into a three-port network), then the denominator would unacceptably vanish (since each port index shows up in each denominator term of Equation 6). Additionally, a number other than zero would lead to conservation of energy problems. Attempting to produce a 3×4 matrix formalism, which builds in the non-transmission to a forth port, leads to the same problem. [0045] Another possible solution is to create a four-port device from a three-port DUT. For example, as shown in FIG. 7, a splitter [0046] A solution of using a substantially lossless and perfectly matched device up front would make things easier in that a second de-embedding step is not required. The losslessness results in a non-reciprocal device that fortunately removes the symmetry problem of the splitter implementation, discussed above. In one embodiment, such a device is a circulator, which is a device that causes signal flow in only one direction (either clockwise or counter clockwise). [0047] Referring to the embodiment of FIG. 8, a circulator [0048] The S-matrix associated with DUT [0049] When circulator [0050] Embedding of circulator [0051] The S-matrix associated with artificial four-port DUT [0052] Based on the definition of S-parameters, the S-parameters of the first row of the S-matrix of Equation 8 all relate to signals leaving port [0053] Based on the definition of S-parameters, the S-parameters of the second column of the S-matrix of Equation 8 all relate to signals being injected into port [0054] Based on the above realizations regarding the first row and the second column of the S-matrix of Equation. 8, it is clear that the seven S-parameters associated with the first row and the second column of the S-matrix are “don't cares.” These are “don't cares” because these S-parameters do not impact the behavior of artificial four-port device [0055] This leaves nine remaining S-parameters that need to be determined for artificial four-port DUT [0056] The S-parameters of artificial four-port DUT [0057] The S-matrix of Equation 9 is a 4×4 matrix that is representative of artificial four-port DUT [0058] Using the S-matrix of Equation 9, four-port embedding and de-embedding techniques can now be performed. Balanced four-port network [0059] Assume Equation 10 is a composite S-matrix representative of four-port DUT [0060]FIG. 9 illustrates the embedding of four-port network [0061] In the discussion of FIG. 8 and Equation [0062] The above discussion is summarized in a flow chart of FIG. 10, which illustrates a method [0063] At a step [0064] At a next step [0065] Finally, at a step [0066]FIG. 11 is a flow diagram that illustrates a method [0067] At a step [0068] At a next step [0069] Finally, at a step [0070] The flow diagram of FIG. 12 shall now be used to describe further details of step [0071] At a step [0072] At a step [0073] At a step [0074] At a step [0075] If the desire is to de-embed the four-port network as called for in step [0076] Steps [0077] Specific embodiments discussed above explain how to embed/de-embed a four-port network into/from a three-port DUT. However, those of ordinary skill in the art reading the above description will appreciate that the use of a circulator to embed/de-embed other networks having an odd number of ports into/from other DUTs having an even number of ports are within the spirit and scope of the present invention. [0078] The foregoing description of the preferred embodiments has been provided to enable any person skilled in the art to make or use the present invention. While the invention has been particularly shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention. [0079] The present invention has been described above with the aid of flow diagrams illustrating the performance of specified steps and relationships thereof. The boundaries of the blocks within the flow diagrams have often been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified steps and relationships thereof are appropriately performed. Any such alternate boundaries are thus within the scope and spirit of the claimed invention. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents. Referenced by
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